summaryrefslogtreecommitdiff
path: root/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/igamma_inverse.hpp
diff options
context:
space:
mode:
Diffstat (limited to 'inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/igamma_inverse.hpp')
-rw-r--r--inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/igamma_inverse.hpp551
1 files changed, 0 insertions, 551 deletions
diff --git a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/igamma_inverse.hpp b/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/igamma_inverse.hpp
deleted file mode 100644
index fd0189ca6..000000000
--- a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/igamma_inverse.hpp
+++ /dev/null
@@ -1,551 +0,0 @@
-// (C) Copyright John Maddock 2006.
-// Use, modification and distribution are subject to the
-// Boost Software License, Version 1.0. (See accompanying file
-// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#ifndef BOOST_MATH_SPECIAL_FUNCTIONS_IGAMMA_INVERSE_HPP
-#define BOOST_MATH_SPECIAL_FUNCTIONS_IGAMMA_INVERSE_HPP
-
-#ifdef _MSC_VER
-#pragma once
-#endif
-
-#include <boost/math/tools/tuple.hpp>
-#include <boost/math/special_functions/gamma.hpp>
-#include <boost/math/special_functions/sign.hpp>
-#include <boost/math/tools/roots.hpp>
-#include <boost/math/policies/error_handling.hpp>
-
-namespace boost{ namespace math{
-
-namespace detail{
-
-template <class T>
-T find_inverse_s(T p, T q)
-{
- //
- // Computation of the Incomplete Gamma Function Ratios and their Inverse
- // ARMIDO R. DIDONATO and ALFRED H. MORRIS, JR.
- // ACM Transactions on Mathematical Software, Vol. 12, No. 4,
- // December 1986, Pages 377-393.
- //
- // See equation 32.
- //
- BOOST_MATH_STD_USING
- T t;
- if(p < 0.5)
- {
- t = sqrt(-2 * log(p));
- }
- else
- {
- t = sqrt(-2 * log(q));
- }
- static const double a[4] = { 3.31125922108741, 11.6616720288968, 4.28342155967104, 0.213623493715853 };
- static const double b[5] = { 1, 6.61053765625462, 6.40691597760039, 1.27364489782223, 0.3611708101884203e-1 };
- T s = t - tools::evaluate_polynomial(a, t) / tools::evaluate_polynomial(b, t);
- if(p < 0.5)
- s = -s;
- return s;
-}
-
-template <class T>
-T didonato_SN(T a, T x, unsigned N, T tolerance = 0)
-{
- //
- // Computation of the Incomplete Gamma Function Ratios and their Inverse
- // ARMIDO R. DIDONATO and ALFRED H. MORRIS, JR.
- // ACM Transactions on Mathematical Software, Vol. 12, No. 4,
- // December 1986, Pages 377-393.
- //
- // See equation 34.
- //
- T sum = 1;
- if(N >= 1)
- {
- T partial = x / (a + 1);
- sum += partial;
- for(unsigned i = 2; i <= N; ++i)
- {
- partial *= x / (a + i);
- sum += partial;
- if(partial < tolerance)
- break;
- }
- }
- return sum;
-}
-
-template <class T, class Policy>
-inline T didonato_FN(T p, T a, T x, unsigned N, T tolerance, const Policy& pol)
-{
- //
- // Computation of the Incomplete Gamma Function Ratios and their Inverse
- // ARMIDO R. DIDONATO and ALFRED H. MORRIS, JR.
- // ACM Transactions on Mathematical Software, Vol. 12, No. 4,
- // December 1986, Pages 377-393.
- //
- // See equation 34.
- //
- BOOST_MATH_STD_USING
- T u = log(p) + boost::math::lgamma(a + 1, pol);
- return exp((u + x - log(didonato_SN(a, x, N, tolerance))) / a);
-}
-
-template <class T, class Policy>
-T find_inverse_gamma(T a, T p, T q, const Policy& pol, bool* p_has_10_digits)
-{
- //
- // In order to understand what's going on here, you will
- // need to refer to:
- //
- // Computation of the Incomplete Gamma Function Ratios and their Inverse
- // ARMIDO R. DIDONATO and ALFRED H. MORRIS, JR.
- // ACM Transactions on Mathematical Software, Vol. 12, No. 4,
- // December 1986, Pages 377-393.
- //
- BOOST_MATH_STD_USING
-
- T result;
- *p_has_10_digits = false;
-
- if(a == 1)
- {
- result = -log(q);
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else if(a < 1)
- {
- T g = boost::math::tgamma(a, pol);
- T b = q * g;
- BOOST_MATH_INSTRUMENT_VARIABLE(g);
- BOOST_MATH_INSTRUMENT_VARIABLE(b);
- if((b > 0.6) || ((b >= 0.45) && (a >= 0.3)))
- {
- // DiDonato & Morris Eq 21:
- //
- // There is a slight variation from DiDonato and Morris here:
- // the first form given here is unstable when p is close to 1,
- // making it impossible to compute the inverse of Q(a,x) for small
- // q. Fortunately the second form works perfectly well in this case.
- //
- T u;
- if((b * q > 1e-8) && (q > 1e-5))
- {
- u = pow(p * g * a, 1 / a);
- BOOST_MATH_INSTRUMENT_VARIABLE(u);
- }
- else
- {
- u = exp((-q / a) - constants::euler<T>());
- BOOST_MATH_INSTRUMENT_VARIABLE(u);
- }
- result = u / (1 - (u / (a + 1)));
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else if((a < 0.3) && (b >= 0.35))
- {
- // DiDonato & Morris Eq 22:
- T t = exp(-constants::euler<T>() - b);
- T u = t * exp(t);
- result = t * exp(u);
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else if((b > 0.15) || (a >= 0.3))
- {
- // DiDonato & Morris Eq 23:
- T y = -log(b);
- T u = y - (1 - a) * log(y);
- result = y - (1 - a) * log(u) - log(1 + (1 - a) / (1 + u));
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else if (b > 0.1)
- {
- // DiDonato & Morris Eq 24:
- T y = -log(b);
- T u = y - (1 - a) * log(y);
- result = y - (1 - a) * log(u) - log((u * u + 2 * (3 - a) * u + (2 - a) * (3 - a)) / (u * u + (5 - a) * u + 2));
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else
- {
- // DiDonato & Morris Eq 25:
- T y = -log(b);
- T c1 = (a - 1) * log(y);
- T c1_2 = c1 * c1;
- T c1_3 = c1_2 * c1;
- T c1_4 = c1_2 * c1_2;
- T a_2 = a * a;
- T a_3 = a_2 * a;
-
- T c2 = (a - 1) * (1 + c1);
- T c3 = (a - 1) * (-(c1_2 / 2) + (a - 2) * c1 + (3 * a - 5) / 2);
- T c4 = (a - 1) * ((c1_3 / 3) - (3 * a - 5) * c1_2 / 2 + (a_2 - 6 * a + 7) * c1 + (11 * a_2 - 46 * a + 47) / 6);
- T c5 = (a - 1) * (-(c1_4 / 4)
- + (11 * a - 17) * c1_3 / 6
- + (-3 * a_2 + 13 * a -13) * c1_2
- + (2 * a_3 - 25 * a_2 + 72 * a - 61) * c1 / 2
- + (25 * a_3 - 195 * a_2 + 477 * a - 379) / 12);
-
- T y_2 = y * y;
- T y_3 = y_2 * y;
- T y_4 = y_2 * y_2;
- result = y + c1 + (c2 / y) + (c3 / y_2) + (c4 / y_3) + (c5 / y_4);
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- if(b < 1e-28f)
- *p_has_10_digits = true;
- }
- }
- else
- {
- // DiDonato and Morris Eq 31:
- T s = find_inverse_s(p, q);
-
- BOOST_MATH_INSTRUMENT_VARIABLE(s);
-
- T s_2 = s * s;
- T s_3 = s_2 * s;
- T s_4 = s_2 * s_2;
- T s_5 = s_4 * s;
- T ra = sqrt(a);
-
- BOOST_MATH_INSTRUMENT_VARIABLE(ra);
-
- T w = a + s * ra + (s * s -1) / 3;
- w += (s_3 - 7 * s) / (36 * ra);
- w -= (3 * s_4 + 7 * s_2 - 16) / (810 * a);
- w += (9 * s_5 + 256 * s_3 - 433 * s) / (38880 * a * ra);
-
- BOOST_MATH_INSTRUMENT_VARIABLE(w);
-
- if((a >= 500) && (fabs(1 - w / a) < 1e-6))
- {
- result = w;
- *p_has_10_digits = true;
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else if (p > 0.5)
- {
- if(w < 3 * a)
- {
- result = w;
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else
- {
- T D = (std::max)(T(2), T(a * (a - 1)));
- T lg = boost::math::lgamma(a, pol);
- T lb = log(q) + lg;
- if(lb < -D * 2.3)
- {
- // DiDonato and Morris Eq 25:
- T y = -lb;
- T c1 = (a - 1) * log(y);
- T c1_2 = c1 * c1;
- T c1_3 = c1_2 * c1;
- T c1_4 = c1_2 * c1_2;
- T a_2 = a * a;
- T a_3 = a_2 * a;
-
- T c2 = (a - 1) * (1 + c1);
- T c3 = (a - 1) * (-(c1_2 / 2) + (a - 2) * c1 + (3 * a - 5) / 2);
- T c4 = (a - 1) * ((c1_3 / 3) - (3 * a - 5) * c1_2 / 2 + (a_2 - 6 * a + 7) * c1 + (11 * a_2 - 46 * a + 47) / 6);
- T c5 = (a - 1) * (-(c1_4 / 4)
- + (11 * a - 17) * c1_3 / 6
- + (-3 * a_2 + 13 * a -13) * c1_2
- + (2 * a_3 - 25 * a_2 + 72 * a - 61) * c1 / 2
- + (25 * a_3 - 195 * a_2 + 477 * a - 379) / 12);
-
- T y_2 = y * y;
- T y_3 = y_2 * y;
- T y_4 = y_2 * y_2;
- result = y + c1 + (c2 / y) + (c3 / y_2) + (c4 / y_3) + (c5 / y_4);
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else
- {
- // DiDonato and Morris Eq 33:
- T u = -lb + (a - 1) * log(w) - log(1 + (1 - a) / (1 + w));
- result = -lb + (a - 1) * log(u) - log(1 + (1 - a) / (1 + u));
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- }
- }
- else
- {
- T z = w;
- T ap1 = a + 1;
- T ap2 = a + 2;
- if(w < 0.15f * ap1)
- {
- // DiDonato and Morris Eq 35:
- T v = log(p) + boost::math::lgamma(ap1, pol);
- z = exp((v + w) / a);
- s = boost::math::log1p(z / ap1 * (1 + z / ap2), pol);
- z = exp((v + z - s) / a);
- s = boost::math::log1p(z / ap1 * (1 + z / ap2), pol);
- z = exp((v + z - s) / a);
- s = boost::math::log1p(z / ap1 * (1 + z / ap2 * (1 + z / (a + 3))), pol);
- z = exp((v + z - s) / a);
- BOOST_MATH_INSTRUMENT_VARIABLE(z);
- }
-
- if((z <= 0.01 * ap1) || (z > 0.7 * ap1))
- {
- result = z;
- if(z <= 0.002 * ap1)
- *p_has_10_digits = true;
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- else
- {
- // DiDonato and Morris Eq 36:
- T ls = log(didonato_SN(a, z, 100, T(1e-4)));
- T v = log(p) + boost::math::lgamma(ap1, pol);
- z = exp((v + z - ls) / a);
- result = z * (1 - (a * log(z) - z - v + ls) / (a - z));
-
- BOOST_MATH_INSTRUMENT_VARIABLE(result);
- }
- }
- }
- return result;
-}
-
-template <class T, class Policy>
-struct gamma_p_inverse_func
-{
- gamma_p_inverse_func(T a_, T p_, bool inv) : a(a_), p(p_), invert(inv)
- {
- //
- // If p is too near 1 then P(x) - p suffers from cancellation
- // errors causing our root-finding algorithms to "thrash", better
- // to invert in this case and calculate Q(x) - (1-p) instead.
- //
- // Of course if p is *very* close to 1, then the answer we get will
- // be inaccurate anyway (because there's not enough information in p)
- // but at least we will converge on the (inaccurate) answer quickly.
- //
- if(p > 0.9)
- {
- p = 1 - p;
- invert = !invert;
- }
- }
-
- boost::math::tuple<T, T, T> operator()(const T& x)const
- {
- BOOST_FPU_EXCEPTION_GUARD
- //
- // Calculate P(x) - p and the first two derivates, or if the invert
- // flag is set, then Q(x) - q and it's derivatives.
- //
- typedef typename policies::evaluation<T, Policy>::type value_type;
- // typedef typename lanczos::lanczos<T, Policy>::type evaluation_type;
- typedef typename policies::normalise<
- Policy,
- policies::promote_float<false>,
- policies::promote_double<false>,
- policies::discrete_quantile<>,
- policies::assert_undefined<> >::type forwarding_policy;
-
- BOOST_MATH_STD_USING // For ADL of std functions.
-
- T f, f1;
- value_type ft;
- f = static_cast<T>(boost::math::detail::gamma_incomplete_imp(
- static_cast<value_type>(a),
- static_cast<value_type>(x),
- true, invert,
- forwarding_policy(), &ft));
- f1 = static_cast<T>(ft);
- T f2;
- T div = (a - x - 1) / x;
- f2 = f1;
- if((fabs(div) > 1) && (tools::max_value<T>() / fabs(div) < f2))
- {
- // overflow:
- f2 = -tools::max_value<T>() / 2;
- }
- else
- {
- f2 *= div;
- }
-
- if(invert)
- {
- f1 = -f1;
- f2 = -f2;
- }
-
- return boost::math::make_tuple(static_cast<T>(f - p), f1, f2);
- }
-private:
- T a, p;
- bool invert;
-};
-
-template <class T, class Policy>
-T gamma_p_inv_imp(T a, T p, const Policy& pol)
-{
- BOOST_MATH_STD_USING // ADL of std functions.
-
- static const char* function = "boost::math::gamma_p_inv<%1%>(%1%, %1%)";
-
- BOOST_MATH_INSTRUMENT_VARIABLE(a);
- BOOST_MATH_INSTRUMENT_VARIABLE(p);
-
- if(a <= 0)
- return policies::raise_domain_error<T>(function, "Argument a in the incomplete gamma function inverse must be >= 0 (got a=%1%).", a, pol);
- if((p < 0) || (p > 1))
- return policies::raise_domain_error<T>(function, "Probabilty must be in the range [0,1] in the incomplete gamma function inverse (got p=%1%).", p, pol);
- if(p == 1)
- return policies::raise_overflow_error<T>(function, 0, Policy());
- if(p == 0)
- return 0;
- bool has_10_digits;
- T guess = detail::find_inverse_gamma<T>(a, p, 1 - p, pol, &has_10_digits);
- if((policies::digits<T, Policy>() <= 36) && has_10_digits)
- return guess;
- T lower = tools::min_value<T>();
- if(guess <= lower)
- guess = tools::min_value<T>();
- BOOST_MATH_INSTRUMENT_VARIABLE(guess);
- //
- // Work out how many digits to converge to, normally this is
- // 2/3 of the digits in T, but if the first derivative is very
- // large convergence is slow, so we'll bump it up to full
- // precision to prevent premature termination of the root-finding routine.
- //
- unsigned digits = policies::digits<T, Policy>();
- if(digits < 30)
- {
- digits *= 2;
- digits /= 3;
- }
- else
- {
- digits /= 2;
- digits -= 1;
- }
- if((a < 0.125) && (fabs(gamma_p_derivative(a, guess, pol)) > 1 / sqrt(tools::epsilon<T>())))
- digits = policies::digits<T, Policy>() - 2;
- //
- // Go ahead and iterate:
- //
- boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
- guess = tools::halley_iterate(
- detail::gamma_p_inverse_func<T, Policy>(a, p, false),
- guess,
- lower,
- tools::max_value<T>(),
- digits,
- max_iter);
- policies::check_root_iterations<T>(function, max_iter, pol);
- BOOST_MATH_INSTRUMENT_VARIABLE(guess);
- if(guess == lower)
- guess = policies::raise_underflow_error<T>(function, "Expected result known to be non-zero, but is smaller than the smallest available number.", pol);
- return guess;
-}
-
-template <class T, class Policy>
-T gamma_q_inv_imp(T a, T q, const Policy& pol)
-{
- BOOST_MATH_STD_USING // ADL of std functions.
-
- static const char* function = "boost::math::gamma_q_inv<%1%>(%1%, %1%)";
-
- if(a <= 0)
- return policies::raise_domain_error<T>(function, "Argument a in the incomplete gamma function inverse must be >= 0 (got a=%1%).", a, pol);
- if((q < 0) || (q > 1))
- return policies::raise_domain_error<T>(function, "Probabilty must be in the range [0,1] in the incomplete gamma function inverse (got q=%1%).", q, pol);
- if(q == 0)
- return policies::raise_overflow_error<T>(function, 0, Policy());
- if(q == 1)
- return 0;
- bool has_10_digits;
- T guess = detail::find_inverse_gamma<T>(a, 1 - q, q, pol, &has_10_digits);
- if((policies::digits<T, Policy>() <= 36) && has_10_digits)
- return guess;
- T lower = tools::min_value<T>();
- if(guess <= lower)
- guess = tools::min_value<T>();
- //
- // Work out how many digits to converge to, normally this is
- // 2/3 of the digits in T, but if the first derivative is very
- // large convergence is slow, so we'll bump it up to full
- // precision to prevent premature termination of the root-finding routine.
- //
- unsigned digits = policies::digits<T, Policy>();
- if(digits < 30)
- {
- digits *= 2;
- digits /= 3;
- }
- else
- {
- digits /= 2;
- digits -= 1;
- }
- if((a < 0.125) && (fabs(gamma_p_derivative(a, guess, pol)) > 1 / sqrt(tools::epsilon<T>())))
- digits = policies::digits<T, Policy>();
- //
- // Go ahead and iterate:
- //
- boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
- guess = tools::halley_iterate(
- detail::gamma_p_inverse_func<T, Policy>(a, q, true),
- guess,
- lower,
- tools::max_value<T>(),
- digits,
- max_iter);
- policies::check_root_iterations<T>(function, max_iter, pol);
- if(guess == lower)
- guess = policies::raise_underflow_error<T>(function, "Expected result known to be non-zero, but is smaller than the smallest available number.", pol);
- return guess;
-}
-
-} // namespace detail
-
-template <class T1, class T2, class Policy>
-inline typename tools::promote_args<T1, T2>::type
- gamma_p_inv(T1 a, T2 p, const Policy& pol)
-{
- typedef typename tools::promote_args<T1, T2>::type result_type;
- return detail::gamma_p_inv_imp(
- static_cast<result_type>(a),
- static_cast<result_type>(p), pol);
-}
-
-template <class T1, class T2, class Policy>
-inline typename tools::promote_args<T1, T2>::type
- gamma_q_inv(T1 a, T2 p, const Policy& pol)
-{
- typedef typename tools::promote_args<T1, T2>::type result_type;
- return detail::gamma_q_inv_imp(
- static_cast<result_type>(a),
- static_cast<result_type>(p), pol);
-}
-
-template <class T1, class T2>
-inline typename tools::promote_args<T1, T2>::type
- gamma_p_inv(T1 a, T2 p)
-{
- return gamma_p_inv(a, p, policies::policy<>());
-}
-
-template <class T1, class T2>
-inline typename tools::promote_args<T1, T2>::type
- gamma_q_inv(T1 a, T2 p)
-{
- return gamma_q_inv(a, p, policies::policy<>());
-}
-
-} // namespace math
-} // namespace boost
-
-#endif // BOOST_MATH_SPECIAL_FUNCTIONS_IGAMMA_INVERSE_HPP
-
-
-
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-25 00:13:36 +0000